Given that engine spool up time is related to the ability of an aircraft to transition from a 3 degree descent angle to to a specified positive climb gradient in the landing configuration, starting this transition from a lower approach speed would result in a greater time required to achieve the specified positive gradient. The actual time required for the engines to accelerate from flight idle to go-around thrust would not be appreciably affected by the airspeed used, while the time required to reach the required positive climb gradient would.
I believe the instructor might have meant acceleration from stable approach RPMs, not idle. The engine would have lower RPM on lower speed, and as acceleration rate is slower on lower RPM, every % less RPM will mean more and more time to get through it.
Is this not the reason, btw., that F40 Vref is 1,25*Vs while F30 Vref is 1,30*Vs? (talking about 737) That higher drag in flaps 40 makes for higher N1 on Vref, faster engine acceleration would then allow for a speed closer to actuall stall.